What is the value of (a) for (ax+4y=20) and (9x+12y=61) to have no solution?
Answer and explanation
Correct answer: 3
For two linear equations to have no solution, the condition is \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}\). Here, \(\frac{a}{9}=\frac{4}{12}=\frac{1}{3}\), giving \(a=3\). Also, \(\frac{20}{61}\ne\frac{1}{3}\), so the two lines are distinct and parallel and therefore have no solution. In an exam, first equate the ratios of the variable coefficients to find the parameter, then verify the ratio of the constants.
Frequently asked questions
What is the correct answer to this question?
3
Why is this the correct answer?
For two linear equations to have no solution, the condition is \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}\). Here, \(\frac{a}{9}=\frac{4}{12}=\frac{1}{3}\), giving \(a=3\). Also, \(\frac{20}{61}\ne\frac{1}{3}\), so the two lines are distinct and parallel and therefore have no solution. In an exam, first equate the ratios of the variable coefficients to find the parameter, then verify the ratio of the constants.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Pair of Linear Equations in Two Variables. Topic: Conditions for solvability.
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